Constructions of asymptotically optimal codebooks over Galois rings

Abstract

Abstract: Codebooks with low value of maximum cross-correlation amplitude are widely used in many fields. Four classes of codebooks are constructed by using Gauss sums and Jacobi sums over Galois rings. It is shown that these codebooks are asymptotically optimal with respect to Welch bound, and the codebook parameters are new and flexible. Based on the properties of Galois rings, it can be seen that these results can cover some results on finite fields when special values are taken, which makes new progress in the study of codebooks.

Key words: Galois rings, Gauss sums, Jacobi sums, asymptotically optimal codebooks, Welch bound

CLC Number:

O157.4

XU Dengming , MENG Chen. Constructions of asymptotically optimal codebooks over Galois rings[J]. Journal of Civil Aviation University of China, 2022, 40(5): 59-64.

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